HIV infection involves many different cell types (infected cells, uninfected cells permissive for virus replication, HIV specific immune cells, and others) which interact with each other and whose numbers, in general, depend on time. Because of interaction among its parts, the system automatically arrives at an approximate steady state coincident with the asymptomatic phase of an HIV infection. The replicating virus population remains quite constant but exhibits considerable genetic variation in time (and among sampled sequences). Our long-term goal is to use mathematical modeling to aid in understanding how such a system can work. Our approach is to (i) select mathematical models of HIV infection based on the criterion that all their predictions agree with the known features of HIV pathogenesis in representative individuals and (ii) formulate predictions for new experiments to test the models. This strategy of "multiple match" has been successfully used in the physical sciences for dealing with complex systems of unknown structure, but it is only being implemented in HIV research. We will apply this strategy to develop models of virus-immune cell interaction in .vivo and explain the mechanism of steady state, and to understand the principal factors of evolution of drug resistance and antigenic escape. At this stage of our research, we will put emphasis on follow-up tests of our models in collaborating groups and design of new tests of updated models. [unreadable] [unreadable] [unreadable]